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NAME

       PZHEGST  - reduce a complex Hermitian-definite generalized eigenproblem
       to standard form

SYNOPSIS

       SUBROUTINE PZHEGST( IBTYPE, UPLO, N, A,  IA,  JA,  DESCA,  B,  IB,  JB,
                           DESCB, SCALE, INFO )

           CHARACTER       UPLO

           INTEGER         IA, IB, IBTYPE, INFO, JA, JB, N

           DOUBLE          PRECISION SCALE

           INTEGER         DESCA( * ), DESCB( * )

           COMPLEX*16      A( * ), B( * )

PURPOSE

       PZHEGST  reduces  a complex Hermitian-definite generalized eigenproblem
       to standard form.

       In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub(  B
       ) denotes B( IB:IB+N-1, JB:JB+N-1 ).

       If  IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, and sub(
       A ) is overwritten  by  inv(U**H)*sub(  A  )*inv(U)  or  inv(L)*sub(  A
       )*inv(L**H)

       If  IBTYPE  =  2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or
       sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by U*sub( A
       )*U**H or L**H*sub( A )*L.

       sub(  B  )  must have been previously factorized as U**H*U or L*L**H by
       PZPOTRF.

       Notes
       =====

       Each global data object  is  described  by  an  associated  description
       vector.   This  vector stores the information required to establish the
       mapping between an object element and  its  corresponding  process  and
       memory location.

       Let  A  be  a generic term for any 2D block cyclicly distributed array.
       Such a global array has an associated description vector DESCA.  In the
       following  comments,  the  character _ should be read as "of the global
       array".

       NOTATION        STORED IN      EXPLANATION
       ---------------  --------------  --------------------------------------
       DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                                      DTYPE_A = 1.
       CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                                      the BLACS process grid A is distribu-
                                      ted over. The context itself is glo-
                                      bal, but the handle (the integer
                                      value) may vary.
       M_A    (global) DESCA( M_ )    The number of rows in the global
                                      array A.
       N_A    (global) DESCA( N_ )    The number of columns in the global
                                      array A.
       MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                                      the rows of the array.
       NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                                      the columns of the array.
       RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                                      row  of  the  array  A  is  distributed.
       CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                                      first column of the array A is
                                      distributed.
       LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                                      array.  LLD_A >= MAX(1,LOCr(M_A)).

       Let K be the number of rows or columns of  a  distributed  matrix,  and
       assume that its process grid has dimension p x q.
       LOCr(  K  )  denotes  the  number of elements of K that a process would
       receive if K were distributed over  the  p  processes  of  its  process
       column.
       Similarly, LOCc( K ) denotes the number of elements of K that a process
       would receive if K were distributed over the q processes of its process
       row.
       The  values  of  LOCr()  and LOCc() may be determined via a call to the
       ScaLAPACK tool function, NUMROC:
               LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
               LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).  An  upper
       bound for these quantities may be computed by:
               LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
               LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

ARGUMENTS

       IBTYPE   (global input) INTEGER
                =  1:  compute  inv(U**H)*sub(  A  )*inv(U)  or  inv(L)*sub( A
                )*inv(L**H); = 2 or 3: compute U*sub( A )*U**H or L**H*sub(  A
                )*L.

       UPLO    (global input) CHARACTER
               =  ’U’:   Upper  triangle of sub( A ) is stored and sub( B ) is
               factored as U**H*U; = ’L’:  Lower  triangle  of  sub(  A  )  is
               stored and sub( B ) is factored as L*L**H.

       N       (global input) INTEGER
               The order of the matrices sub( A ) and sub( B ).  N >= 0.

       A       (local input/local output) COMPLEX*16 pointer into the
               local  memory  to  an array of dimension (LLD_A, LOCc(JA+N-1)).
               On entry, this array contains the local pieces  of  the  N-by-N
               Hermitian  distributed  matrix  sub(  A  ).  If UPLO = ’U’, the
               leading N-by-N upper triangular part of sub( A )  contains  the
               upper  triangular  part  of  the matrix, and its strictly lower
               triangular part is not referenced.  If UPLO = ’L’, the  leading
               N-by-N  lower  triangular  part  of sub( A ) contains the lower
               triangular  part  of  the  matrix,  and  its   strictly   upper
               triangular part is not referenced.

               On  exit,  if  INFO  = 0, the transformed matrix, stored in the
               same format as sub( A ).

       IA      (global input) INTEGER
               A’s global row index, which points  to  the  beginning  of  the
               submatrix which is to be operated on.

       JA      (global input) INTEGER
               A’s  global  column index, which points to the beginning of the
               submatrix which is to be operated on.

       DESCA   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix A.

       B       (local input) COMPLEX*16 pointer into the local memory
               to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry,  this
               array  contains  the local pieces of the triangular factor from
               the Cholesky factorization of sub( B ), as returned by PZPOTRF.

       IB      (global input) INTEGER
               B’s  global  row  index,  which  points to the beginning of the
               submatrix which is to be operated on.

       JB      (global input) INTEGER
               B’s global column index, which points to the beginning  of  the
               submatrix which is to be operated on.

       DESCB   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix B.

       SCALE   (global output) DOUBLE PRECISION
               Amount  by which the eigenvalues should be scaled to compensate
               for the scaling performed in this routine.  At  present,  SCALE
               is  always  returned  as  1.0, it is returned here to allow for
               future enhancement.

       INFO    (global output) INTEGER
               = 0:  successful exit
               < 0:  If the i-th argument is an array and the j-entry  had  an
               illegal  value, then INFO = -(i*100+j), if the i-th argument is
               a scalar and had an illegal value, then INFO = -i.